(2a+3)(a-3)=-2

Solution for (2a+3)(a-3)=-2 equation:

(2a+3)(a-3)=-2

We move all terms to the left:

(2a+3)(a-3)-(-2)=0

We add all the numbers together, and all the variables

(2a+3)(a-3)+2=0

We multiply parentheses ..

(+2a^2-6a+3a-9)+2=0

We get rid of parentheses

2a^2-6a+3a-9+2=0

We add all the numbers together, and all the variables

2a^2-3a-7=0

a = 2; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·2·(-7)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{65}}{2*2}=\frac{3-\sqrt{65}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{65}}{2*2}=\frac{3+\sqrt{65}}{4}
$